Ram can complete the work in 10 hours, Ajit in 12 hours and Suresh in 15 hours. All of them began the work together, but Ram had

Question

2 months ago

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Ram can complete the work in 10 hours, Ajit in 12 hours and Suresh in 15 hours. All of them began the work together, but Ram had

to leave the work after 2 hours of the start and Ajit left 3 hours before the completion of the work. How long did the work last? Select one:
a. 7 hrs
b. 8 hrs
c. 9 hrs
d. Cannot be determined

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-02-18T01:50:57+03:00

Choice D is correct because Ram contributed only 2 hours of work before departing. Ajit left 3 hours before the overall completion, suggesting some overlap in their working times. As all workers started simultaneously, this doesn't imply Ajit abstained from work; he might have worked for up to 12 hours. However, the exact time each spent working is not specified. Suresh could have worked anywhere up to 15 hours, but the precise duration remains unknown. Apologies if this explanation seems off-topic or incorrect.

Inessa [12.5K] · Answer 2 · 2026-02-18T01:50:44+03:00

Response:

The correct choice is option A.

Stepwise explanation:

Let the total work be represented as W.

Ram can finish the task in 10 hours, Ajit in 12 hours, and Suresh in 15 hours.

$\texttt{Rate of Ram =}\frac{W}{10}\\\\\texttt{Rate of Ajit =}\frac{W}{12}\\\\\texttt{Rate of Suresh =}\frac{W}{15}$

Ram worked for 2 hours before leaving, and Ajit stopped working 3 hours prior to the task's completion.

Let t denote the total time taken to complete the work.

The equation to represent this is:

$W=2\times \frac{W}{10}+(t-3)\times \frac{W}{12}+t\times \frac{W}{15}\\\\1=\frac{1}{5}+\frac{t-3}{12}+\frac{t}{15}\\\\12+5(t-3)+4t=60\\\\9t=63\\\\t=7hours$

Therefore, option A correctly answers the question.